In many applications, noncoherent or differential detection is an attractive alternative to coherent detection due to the simplicity of implementation and/or where the transmission environment is sufficiently degraded, e.g., a multipath fading channel, that acquiring and tracking a coherent demodulation reference signal is difficult if not impossible. A noncoherent detector is a detector that does not directly estimate the phase of the received signal. Although differential detection removes the need for carrier acquisition and tracking in the receiver, it suffers from a performance penalty (additional required SNR at a given bit error rate) when compared to ideal (perfect carrier phase reference) coherent detection. The amount of this performance penalty increases with the number of phases M and is significant for M≥4. Dariush Divsalar and Marvin K. Simon, in their paper entitled “Multiple-Symbol Differential Detection of MPSK,” IEEE Transactions on Communications, March 1990 (the disclosure of which is incorporated by reference in its entirety), presented a differential detection technique involving making a joint decision on several symbols simultaneously as opposed to symbol-by-symbol detection. The multiple symbol differential detection technique is a form of maximum-likelihood sequence estimation and assumes that carrier phase is constant during the extended observation interval, which is typically a reasonable assumption for observations of the order of three or four symbol observations. The multiple symbol differential detector described by Dr. Divsalar and Dr. Simon performs hard decisions. A hard decision is a decision between a fixed set of possible values (e.g. 0 or 1). In a soft output detector, each bit in the output also takes on a value indicating reliability.